Calculate the electric field at origin due to infinite number of charges as shown in figure below.

Explanation

(a) `E_(0)=kq[1/1+1/4+1/16+ ----]=(kq. 1)/((1-1//4))=(4kq)/3 " "[ :' S_(oo)=a/(1-r), a=1 and r=1/4]`
(b) `E_(0)=kq[1/1-1/4+1/16-----]=(kq. 1)/((1-(-1//4)))=(4kq)/5`